the consumer price index is increasing at a rate of 9% per year. what is its doubling time?
8 years, without using a calculator!
The rule of 72 gives doubling time as the quotient of 72 over the interest rate.
An accurate calculation is as follows:
n=number of years:
1.09^n=2
take logs and solve for n:
n=log(2)/log(1.09)
=8.04 years
To find the doubling time of the Consumer Price Index (CPI) increasing at a rate of 9% per year, we can use the Rule of 72.
The Rule of 72 is a simple mathematical formula used to estimate the time it takes for an investment or value to double, given a fixed annual growth rate. It states that by dividing the number 72 by the annual growth rate, you can approximate the doubling time.
In this case, the annual growth rate is 9%. So, to calculate the doubling time, we divide 72 by 9:
D = 72 / R
D = 72 / 9
D = 8 years
Therefore, if the Consumer Price Index is increasing at a rate of 9% per year, it would take approximately 8 years for it to double.